xip

2. Partitioned regression and geometric interpretation. Suppose you regress Y on X and

obtain the fitted values Ỹ. Also, suppose X is partitioned as X = [X₁, X₂], where X₁ and X₂

are both n x 1 vectors. Now, you regress Y on X₁ and Ŷ. Let â be the OLS estimator of the

coefficient on Ŷ. What is the value of â? Provide both analytic and geometric arguments to

support your answer.